### Abstract

Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted):E(t)=E_{0}{A _{1} exp[-(t/τ_{1})^{β}]+(1-A_{1}) exp[-(t/τ_{2})^{γ}]},[0<A_{1},β, γ<1],where E_{0} is the initial modulus value E(0). τ_{1} and τ_{2}(≫τ_{1})are characteristic times of the relaxation, A_{1} is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and β and γ are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.

Original language | English |
---|---|

Pages (from-to) | 1433-1437 |

Number of pages | 5 |

Journal | Journal of Biomechanics |

Volume | 37 |

Issue number | 9 |

DOIs | |

Publication status | Published - Sep 2004 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Orthopedics and Sports Medicine

### Cite this

*Journal of Biomechanics*,

*37*(9), 1433-1437. https://doi.org/10.1016/j.jbiomech.2003.12.023

**Anisotropic viscoelastic properties of cortical bone.** / Iyo, Toshiya; Maki, Yasuyuki; Sasaki, Naoki; Nakata, Mitsuo.

Research output: Contribution to journal › Article

*Journal of Biomechanics*, vol. 37, no. 9, pp. 1433-1437. https://doi.org/10.1016/j.jbiomech.2003.12.023

}

TY - JOUR

T1 - Anisotropic viscoelastic properties of cortical bone

AU - Iyo, Toshiya

AU - Maki, Yasuyuki

AU - Sasaki, Naoki

AU - Nakata, Mitsuo

PY - 2004/9

Y1 - 2004/9

N2 - Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted):E(t)=E0{A 1 exp[-(t/τ1)β]+(1-A1) exp[-(t/τ2)γ]},[0<A1,β, γ<1],where E0 is the initial modulus value E(0). τ1 and τ2(≫τ1)are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and β and γ are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.

AB - Relaxation Young's modulus of cortical bone was investigated for two different directions with respect to the longitudinal axis of bone (bone axis, BA): the modulus parallel (P) and normal (N) to the BA. The relaxation modulus was analyzed by fitting to the empirical equation previously proposed for cortical bones, i.e., a linear combination of two Kohlraush-Williams-Watts (KWW) functions (Iyo et al., 2003. Biorheology, submitted):E(t)=E0{A 1 exp[-(t/τ1)β]+(1-A1) exp[-(t/τ2)γ]},[0<A1,β, γ<1],where E0 is the initial modulus value E(0). τ1 and τ2(≫τ1)are characteristic times of the relaxation, A1 is the fractional contribution of the fast relaxation (KWW1 process) to the whole relaxation process, and β and γ are parameters describing the shape of the relaxation modulus. In both P and N samples, the relaxation modulus was described well by the empirical equation. The KWW1 process of a P sample almost completely coincided with that of an N sample. In the slow process (KWW2 process), there was a difference between the relaxation modulus of a P sample and that of an N sample. The results indicate that the KWW1 process in the empirical equation represents the relaxation in the collagen matrix in bone and that the KWW2 process is related to a higher-order structure of bone that is responsible for the anisotropic mechanical properties of bone.

UR - http://www.scopus.com/inward/record.url?scp=3242741106&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=3242741106&partnerID=8YFLogxK

U2 - 10.1016/j.jbiomech.2003.12.023

DO - 10.1016/j.jbiomech.2003.12.023

M3 - Article

VL - 37

SP - 1433

EP - 1437

JO - Journal of Biomechanics

JF - Journal of Biomechanics

SN - 0021-9290

IS - 9

ER -